- Email: [email protected]
Thermoelectric power of NiCu and NiRh alloys
Solid State Cominunications,Vol. 20, pp. 1—4, 1976.
Pergamon Press.
Printed in Great Britain
THERMOELECTRIC POWER OF NiCu AND NiRh ALLOYS*t J.S. Touge4 and M.P. Sarachik City College of the City University of New York, NY 10031, U.S.A. (Received 5 August 1975 by A.G. Chynoweth) Thermoelectric power data between 4.2 and 300°K are presented for NiCu alloys and NiRh alloys near their critical compositions for ferromagnetism. 1. INTRODUCTION
By contrast, the resistivity11 of Ni—Rh increases monotonically with temperature a transition from T2 to linear T dependence occursand at low temperatures.
NEUTRON SCATTERING1 and susceptibility2’3 measurements have shown that large magnetic polarization clouds extending over many atoms exist in ferromagnetic Ni—Cu and Ni—Rh alloys, and that these superparamagnetic clusters persist well into the paramagnetic composition range. Despite the similarities in their magnetic properties, the resistivities of Ni—Cu and Ni—Rh are markedly different. The resistivity of Ni—Cu alloys near the critical composition for ferromagnetism displays two minima, one46 at 50—80°K (depending on composition), and another7 at about 600°K, which is approximately the Curie temperature of Ni. This behavior has been attributed7’8 to the existence and effects of giant spin clusters. In a calculation treating both inter- and intra-cluster interactions, Levin and Mffls8 showed that the spin disorder resistivity decreases with increasing temperature, producing the minimum observed at 600°K. The low-temperature minimum has been attributed8’9 to the spin—ifip scattering of conduction electrons from rigid clusters, giving rise to a Kondotype effect. However, similar behavior, although much less pronounced, has been observed by Ahmad and Greig’°in Pd~Ag~, which has no spin clusters. These authors attribute the behavior of the resistivity of this alloy to a reduction in s—d interband scattering with increasing temperature, and they suggest that this mechanism may contribute to the minima in Ni—Cu which is chemically similar.
*
Behavior similar to that of Ni—Rh has been observed’2 for other Ni-based transition metal alloys which have polarization clouds, such as Ni—V, Ni—Mo and Ni—Ru, and for dilute alloys such as Rh(Fe),13 Ir(Fe)’4 and Pd(Ni)~which have spin fluctuations due to nearly magnetic impurities.16”7 It hasofbeen suggested3 that the behavior of the resistivity Ni—Rh may be attributed to fluctuations associated with nearly magnetic clusters. In this paper we present the results of thermoelectric power measurements between 4.2°K and room temperature forcomposition a series of Ni—Cu and Ni—Rh alloys near the critical for ferromagnetism. 2. EXPERIMENTAL PROCEDURE AND RESULTS The samples used in the present experiments were the small rods used for resistivity studies by Houghton et al. Since they were approximately four years old, some Ni—Cu samples were reannealed for two days at 900°Cand quenched in iced brine. Measurements were performed between 4.2 and 300°K using standard techniques. The sample was anchored at one end to a heat sink and a temperature gradient was established by a heater mounted at the free end of the sample. Copper— constantan thermocouples were used to determine the temperature T and temperature gradient ~T, and a sensitive nanovoltmeter was used to measure the potential difference ~V. The estimated overall error in the measured thermoelectric power is less than 2%. The thermoelectric power of Ni—Cu alloys ranging in composition from 30 to 50 at.%Ni is shown as a function of temperature in Fig. 1. (The critical compo~
Supported by AFOSR from 1970 to 1972 and by the National Science Foundation from 1972 to 1974.
t Based on part of a dissertation submitted to the
sition is NL~Cu 56). Careful examination reveals a defmite change in slope in the vicinity of 50°K for all compositions. The Ni42 Cu58 alloy was measured most carefully in a total of twelve separate runs, and the data
graduate school at City College of the City University of New York by J .S. Touger in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
for this alloy show a small but unmistakable “kink” between 40 and 50°K. This kink was reproducible, and was not present for the thermoelectric power of a sample
~ Present Address: Division of Science, Curry College, Milton, MA 02186, U.S.A. 1
2 20
40
60
THERMOELECTRIC POWER OF NiCu AND NiRh ALLOYS 80 100 120 140 0 °-~o-....L0_I
Vol. 20, No. 1 I
______
-4
I
53K “— •.-~-%.
0 8 12
—4 0
°“~
~
~
—t...-..._
76K 15K
0 20 -24 116
-40
-40
\\
—40
~
T
300K
297K 200D K
,-~
Cu 20 40 60 80 Ni __________________________________ Ni CONCENTRATION I I (°I~)
28 24
38’/~NI -24
~ ‘\‘.~.a..-’ D—..
Fig. 2. Thermoelectric power of Ni—Cu as a function
28 ~ w 0
42°I.~
0 —
4
•
32
—28
of Nitaken several and temperatures. Data points are from: o at Zrudsky Showalter (reference 17); ~concentration Schroeder, Wolfand Woollam (reference 19); ci Ahmad and Greig (reference 20);. present experiment. —
—
—
—
0 431N1 -32 0
__________________________________________
28
w
o~
~6~Nf
-20 -16
32 28 32
16
-32 50’/,Ni ‘28
4
I
-32 -24 -28
0
-36 ~_ ~-30
-36 ~~6%Ni~.NiI
40
0
~
U
1
~NI14
•_—
~NI
•~
~
-40 ~5O~~)
14
2
00f• w 0’
250
20 40 60 80 100 120 TEMPERATURE C ‘1< )
.•~.
140
Fig. 1. Thermoelectric power as a function of temperature for Ni—Cu alloys containing between 30 and SOat.%Ni. Note that a broken scale is used to separate the curves for clarity, and lines are drawn as a guide to the eye. The crosses are data for a freshly annealed sample of Ni42 Cues. The inset shows data to 300°K for Ni% Cu5., and is typical of all other curves in this temperature range. of pure Pd, which was measured after each two or three runs of the Ni42 Cu58 sample. The other alloy compositions were run fewer times, and the scatter in the data is consequently greater. A change in slope is still clearly there, however, and there are suggestions of similar kinks at 40—50°K for the alloys near the critical cornposition (38, 43 and 46 at. Ni).same Datatemperature obtained by range 8 in% the Zrudsky and Showalter’ for Ni—Cu alloys with lower Ni concentrations (6.2, 11.6 and 23.6 at.%Ni) showed no such behavior, Legvold et al.19 noted that low temperature resistivity measurements on freshly annealed Ni differed numerically from measurements on44a Cu56 sample which was three years old, though qualitatively the
U I ~
~.“ •.
•~
0
4
•~..—•‘
/ o
I
3 50
100 150 200 TEMPERATURE (K)
250
Fig. 3. Thermoelectric power as a function of temperature for Ni—Rh alloys containing between 56 and 64 64 at. % Ni. Note that a broken scale is used to separate the curves for clarity, and lines are drawn as a guide to the eye. curves were not significantly changed. Since our samples were four years old; we reannealed and remeasured the Ni42 Cu58 sample, and the results up to 150°K are plotted as crosses in Fig. 1. The data before and after annealing agree between 140 and 300°K to within 1/2%. The effect at about 50°K, although somewhat smaller for the freshly annealed sample, is stifi clearly there. The thermoelectric power of Ni—Cu is plotted as a function of Ni concentration in Fig. 2, using the ternperature as a parameter. The data of Zrudsky and 8 are included,as well as data obtained at Showalter’ 300°K by Schroeder et al.2°for low Ni concentrations and by Ahmad and Greig2’ for intermediate
Vol. 20, No. 1
THERMOELECTRIC POWER OF NiCu AND NiRh ALLOYS
concentrations. Our data at 297°K fit well with results of Zrudsky and Showalter at low concentrations, but numerical values differ somewhat from the 300°K data of Ahmad and Greig at higher concentrations, though the behavior agrees qualitatively. Better agreement is obtained with data of Chévenard,22 after correcting for the fact that his measurements were obtained relative to Pt (a fact which has been omitted in some more recent references23). These numerical discrepancies are very likely due to metallurgical differences other than different shelf lifetimes, which as mentioned earlier, cause changes of less than 1/2% at 300°K. The thermoelectric power of Ni—Rh alloys ranging in composition from 56 to 64 at.% Ni is shown as a function of temperature in Fig. 3. (The critical composition is Ni63 Rh37). Although no kinks of the type found for Ni—Cu are in evidence here, there does appear to be a change in slope at approximately 25°K. 3. DISCUSSION The salient feature of the present results is that, unlike the resistivity, the thermoelectric power of Ni—Cu and Ni—Rh does not exhibit any dramatic behavior and is in the main quite well-behaved. Further, one should note that the thermoelectric power is negative for Ni—Cu and positive for Ni—Rh alloys. The usual explanation for this in terms of a rigid band model is that for transition metals the s—d interband scattering term in the thermoelectric power can dominate, and this term gives a positive or negative contribution depending on whether the d-band density of states near the Fermi energy is increasing or decreasing with energy. As discussed further below, however, it is very unlikely that a band model is even approximately relevant for these alloys. A small anomaly in the thermoelectric power of Ni—Cu occurs at about 50°K, which is the temperature range in which there is a low temperature minimum in 8’9 that the effects minimum the resistivity. This suggests that the two are in related. It has at been the resistivity lowsuggested temperatures arises from spin—ifip scattering of conduction electrons from rigid spin clusters, analogous to Kondo scattering in alloys contaming dilute concentrations of impurity atoms which have a localized moment. One might then expect a contribution to the thermoelectric power which also arises from spin—flip scattering of electrons. This process gives rise in very dilute Kondo alloys to a peak in the thermoelectric power at a temperature which independent of magnetic impurity concentration.24 Susceptibility experiments2 indicate that the concentration of clusters in Ni—Cu is in fact quite low and increases gradually as one approaches the critical composition. In the present experiment we observe an anomaly in the thermoelectric
3
power at about 50°K independent of alloy composition. The fact that the temperature at which the effect occurs stays roughly the same as the cluster concentration varies is thus consistent with the above suggestion. On the other hand, it is intriguing to note that Taylor and Coles25 observed an anomalous temperature dependence for the thermoelectric power of Pd.,~Ag~ similar to what we have found for Ni—Cu. This anomaly was observed in the vicinity of 120°K, and was not in evidence in Pd 44 Ag54 or Pd~Ag.~, the nearest compositions measured. Thus, both the resistivity and the thermoelectric power of the two isoelectronic systems Pd—Ag and Ni—Cu are quite similar, suggesting that they may in fact derive from the same or related causes. Since Pd—Ag does not have spin clusters, the behavior of this system cannot be magnetic in origin. Ahmed and Greig’° propose an explanation for the resistivity based on a band model description, where the two minima arise from temperature dependent s—d interband scattering; they also suggest that the same mechanism may play a 26 however, indicate role in Ni—Cu. Various experiments, that local phenomena predominate in both alloy systems, and that the alloys are essentially described by a superposition of bands appropriate to the two separate constituent metals. Further, a rigid band description of the type proposed by Ahmad and Greig,’°even when modified as they suggest by variations on a local scale, would lead to temperature (i.e. energy) dependences which vary considerably with composition, particularly in light of the presence of an almost filled d-band. Instead, the thermoelectric power exhibits a change in slope at approximately the same temperature of 50°K for a fairly wide range of Ni—Cu compositions. This strongly suggests that the relevant process is local, and not consistent with a band description. In this connection, it would be interesting to obtain measurements for Pd—Ag alloys with compositions close to Pd 60Ag.~. In closing, one should note that the resistivity anomalies in Ni—Cu are an order of magnitude larger than in Pd—Ag, and the anomalies in both the resistivity and thermoelectric power persist over a wide range of Ni—Cu compositions. One should not overlook the possibility that more than one mechanism plays a role in Ni—Cu. Thus, the behavior of Ni—Cu may be determined both by effects due to spin clusters and by a mechanism which is common to Ni—Cu and Pd—Ag.
Acknowledgements The authors are indebted to the referee for his valuable and constructive comments, and for pointing out an erroneous assumption in an earlier version of this article. We also thank Professors Frederick W. Smith and James S. Kouvel for many helpful discussions. —
4
THERMOELECTRIC POWER OF NiCu AND NiRh ALLOYS
vol. 20, No. 1
REFERENCES 1.
HICKS T.J., RAINFORD B., KOUVEL J.S., LOW G.G. & COMLY i.E.,Phys. Rev. Letr. 22,531(1969).
2. 3.
4.
KOUVEL J.S. & COMLY J.B., Phys. Rev. Lett. 24, 598 (1970). MUELLNER W.C. & KOUVEL J.S.,Magnetism and Magnetic Materials 1971 (Edited by GRAHAM C.D. Jr. & RHYNE J.J.) p. 487. AlP Conf. Proc., New York, (1972); MUELLNER W.C. & KOUVEL J.S., Phys. Rev. B! 1, 4552 (1975). HOUGHTON R.W., SARACHIK M,P. & KOUVEL J.S., Solid State Commun. 8,943(1970).
5. 6.
SKOSKIEWICZ T. & BARANOWSKI B., Solid State Commun. 7,647(1969). CRANGLE J. & BUTCHER P.J.L.,Phys. Lett. A32, 80(1970).
7.
HOUGHTON R.W., SARACHIK M.P. & KOUVEL J.S., Phys. Rev. Lett. 25, 238 (1970).
8.
LEVIN K. & MILLS D.L.,Phys. Rev. 89,2354(1974).
—
9. 10.
FIBICH M. & RON A., J. Phys. 32, C1-748 (1971). MIMAD H.M. & GREIG D.,Phys. Rev. Lett. 32,833(1974).
11.
HOUGHTON R.W., SARACHIK M.P. & KOUVEL J.S., Solid State Commun. 10,369(1972).
12. 13.
AMAJ1OU A., GAUTIER F. & LOEGEL B.,J. Phys. 35, C4-217 (1974). COLES B.R.,Phys. Lett. 8,243 (1964).
14.
SARACHIK M.P., Phys. Rev. 170, 679 (1968).
15. 16.
SCHINDLER A.I. & RICE M.J.,Phys. Rev. 164,759(1967). LEDERER P. & MILLS D.L.,Phys. Rev. 165,837 (1968).
17. 18.
KAISER A.B. & DONIACH S.,Int. J. Magn. 1, 11(1970). ZRUDSKY D.R. & SHOWALTER A.B.,Phys. Lett. 45A, 105 (1973).
19. 20.
LEGVOLD S., PETERSON D.T., BURGARDT P., HOFER R.J., LUNDELL B. & VYROSTEK T.A., Phys. Rev. B9, 2386 (1974). SCHROEDER P.A., WOLF R. & WOOLLAM J.A.,Phys. Rev. 138, A105 (1965).
21.
AHMAD H.M. & GREIG D.,J. Phys. 35, C4-223 (1974).
22. 23.
CHEVENARD P., J. Inst. Metals 36, 39 (1926). COLES B.R.,Proc. Phys. Soc. B65, 221 (1952); and later reproduced in ZIMAN J.M., Electrons and Phonons, p. 401. Clarendon Press, Oxford (1962). DAYBELL M.D. & STEYERT W.A., Rev. Mod. Phys. 40,380(1968).
24. 25. 26.
TAYLOR J.C. & COLES B.R.,Phys. Rev. 102,27 (1956). See for example: ROBBINS C.G., CLAUS H. & BECK P.A.,Phys. Rev. Lett. 22, 1307 (1969); HUFNER S., WERTHEIM G.K. & WERNICK J.H., Phys. Rev. B8, 4511(1973).
Pergamon Press.
Printed in Great Britain
THERMOELECTRIC POWER OF NiCu AND NiRh ALLOYS*t J.S. Touge4 and M.P. Sarachik City College of the City University of New York, NY 10031, U.S.A. (Received 5 August 1975 by A.G. Chynoweth) Thermoelectric power data between 4.2 and 300°K are presented for NiCu alloys and NiRh alloys near their critical compositions for ferromagnetism. 1. INTRODUCTION
By contrast, the resistivity11 of Ni—Rh increases monotonically with temperature a transition from T2 to linear T dependence occursand at low temperatures.
NEUTRON SCATTERING1 and susceptibility2’3 measurements have shown that large magnetic polarization clouds extending over many atoms exist in ferromagnetic Ni—Cu and Ni—Rh alloys, and that these superparamagnetic clusters persist well into the paramagnetic composition range. Despite the similarities in their magnetic properties, the resistivities of Ni—Cu and Ni—Rh are markedly different. The resistivity of Ni—Cu alloys near the critical composition for ferromagnetism displays two minima, one46 at 50—80°K (depending on composition), and another7 at about 600°K, which is approximately the Curie temperature of Ni. This behavior has been attributed7’8 to the existence and effects of giant spin clusters. In a calculation treating both inter- and intra-cluster interactions, Levin and Mffls8 showed that the spin disorder resistivity decreases with increasing temperature, producing the minimum observed at 600°K. The low-temperature minimum has been attributed8’9 to the spin—ifip scattering of conduction electrons from rigid clusters, giving rise to a Kondotype effect. However, similar behavior, although much less pronounced, has been observed by Ahmad and Greig’°in Pd~Ag~, which has no spin clusters. These authors attribute the behavior of the resistivity of this alloy to a reduction in s—d interband scattering with increasing temperature, and they suggest that this mechanism may contribute to the minima in Ni—Cu which is chemically similar.
*
Behavior similar to that of Ni—Rh has been observed’2 for other Ni-based transition metal alloys which have polarization clouds, such as Ni—V, Ni—Mo and Ni—Ru, and for dilute alloys such as Rh(Fe),13 Ir(Fe)’4 and Pd(Ni)~which have spin fluctuations due to nearly magnetic impurities.16”7 It hasofbeen suggested3 that the behavior of the resistivity Ni—Rh may be attributed to fluctuations associated with nearly magnetic clusters. In this paper we present the results of thermoelectric power measurements between 4.2°K and room temperature forcomposition a series of Ni—Cu and Ni—Rh alloys near the critical for ferromagnetism. 2. EXPERIMENTAL PROCEDURE AND RESULTS The samples used in the present experiments were the small rods used for resistivity studies by Houghton et al. Since they were approximately four years old, some Ni—Cu samples were reannealed for two days at 900°Cand quenched in iced brine. Measurements were performed between 4.2 and 300°K using standard techniques. The sample was anchored at one end to a heat sink and a temperature gradient was established by a heater mounted at the free end of the sample. Copper— constantan thermocouples were used to determine the temperature T and temperature gradient ~T, and a sensitive nanovoltmeter was used to measure the potential difference ~V. The estimated overall error in the measured thermoelectric power is less than 2%. The thermoelectric power of Ni—Cu alloys ranging in composition from 30 to 50 at.%Ni is shown as a function of temperature in Fig. 1. (The critical compo~
Supported by AFOSR from 1970 to 1972 and by the National Science Foundation from 1972 to 1974.
t Based on part of a dissertation submitted to the
sition is NL~Cu 56). Careful examination reveals a defmite change in slope in the vicinity of 50°K for all compositions. The Ni42 Cu58 alloy was measured most carefully in a total of twelve separate runs, and the data
graduate school at City College of the City University of New York by J .S. Touger in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
for this alloy show a small but unmistakable “kink” between 40 and 50°K. This kink was reproducible, and was not present for the thermoelectric power of a sample
~ Present Address: Division of Science, Curry College, Milton, MA 02186, U.S.A. 1
2 20
40
60
THERMOELECTRIC POWER OF NiCu AND NiRh ALLOYS 80 100 120 140 0 °-~o-....L0_I
Vol. 20, No. 1 I
______
-4
I
53K “— •.-~-%.
0 8 12
—4 0
°“~
~
~
—t...-..._
76K 15K
0 20 -24 116
-40
-40
\\
—40
~
T
300K
297K 200D K
,-~
Cu 20 40 60 80 Ni __________________________________ Ni CONCENTRATION I I (°I~)
28 24
38’/~NI -24
~ ‘\‘.~.a..-’ D—..
Fig. 2. Thermoelectric power of Ni—Cu as a function
28 ~ w 0
42°I.~
0 —
4
•
32
—28
of Nitaken several and temperatures. Data points are from: o at Zrudsky Showalter (reference 17); ~concentration Schroeder, Wolfand Woollam (reference 19); ci Ahmad and Greig (reference 20);. present experiment. —
—
—
—
0 431N1 -32 0
__________________________________________
28
w
o~
~6~Nf
-20 -16
32 28 32
16
-32 50’/,Ni ‘28
4
I
-32 -24 -28
0
-36 ~_ ~-30
-36 ~~6%Ni~.NiI
40
0
~
U
1
~NI14
•_—
~NI
•~
~
-40 ~5O~~)
14
2
00f• w 0’
250
20 40 60 80 100 120 TEMPERATURE C ‘1< )
.•~.
140
Fig. 1. Thermoelectric power as a function of temperature for Ni—Cu alloys containing between 30 and SOat.%Ni. Note that a broken scale is used to separate the curves for clarity, and lines are drawn as a guide to the eye. The crosses are data for a freshly annealed sample of Ni42 Cues. The inset shows data to 300°K for Ni% Cu5., and is typical of all other curves in this temperature range. of pure Pd, which was measured after each two or three runs of the Ni42 Cu58 sample. The other alloy compositions were run fewer times, and the scatter in the data is consequently greater. A change in slope is still clearly there, however, and there are suggestions of similar kinks at 40—50°K for the alloys near the critical cornposition (38, 43 and 46 at. Ni).same Datatemperature obtained by range 8 in% the Zrudsky and Showalter’ for Ni—Cu alloys with lower Ni concentrations (6.2, 11.6 and 23.6 at.%Ni) showed no such behavior, Legvold et al.19 noted that low temperature resistivity measurements on freshly annealed Ni differed numerically from measurements on44a Cu56 sample which was three years old, though qualitatively the
U I ~
~.“ •.
•~
0
4
•~..—•‘
/ o
I
3 50
100 150 200 TEMPERATURE (K)
250
Fig. 3. Thermoelectric power as a function of temperature for Ni—Rh alloys containing between 56 and 64 64 at. % Ni. Note that a broken scale is used to separate the curves for clarity, and lines are drawn as a guide to the eye. curves were not significantly changed. Since our samples were four years old; we reannealed and remeasured the Ni42 Cu58 sample, and the results up to 150°K are plotted as crosses in Fig. 1. The data before and after annealing agree between 140 and 300°K to within 1/2%. The effect at about 50°K, although somewhat smaller for the freshly annealed sample, is stifi clearly there. The thermoelectric power of Ni—Cu is plotted as a function of Ni concentration in Fig. 2, using the ternperature as a parameter. The data of Zrudsky and 8 are included,as well as data obtained at Showalter’ 300°K by Schroeder et al.2°for low Ni concentrations and by Ahmad and Greig2’ for intermediate
Vol. 20, No. 1
THERMOELECTRIC POWER OF NiCu AND NiRh ALLOYS
concentrations. Our data at 297°K fit well with results of Zrudsky and Showalter at low concentrations, but numerical values differ somewhat from the 300°K data of Ahmad and Greig at higher concentrations, though the behavior agrees qualitatively. Better agreement is obtained with data of Chévenard,22 after correcting for the fact that his measurements were obtained relative to Pt (a fact which has been omitted in some more recent references23). These numerical discrepancies are very likely due to metallurgical differences other than different shelf lifetimes, which as mentioned earlier, cause changes of less than 1/2% at 300°K. The thermoelectric power of Ni—Rh alloys ranging in composition from 56 to 64 at.% Ni is shown as a function of temperature in Fig. 3. (The critical composition is Ni63 Rh37). Although no kinks of the type found for Ni—Cu are in evidence here, there does appear to be a change in slope at approximately 25°K. 3. DISCUSSION The salient feature of the present results is that, unlike the resistivity, the thermoelectric power of Ni—Cu and Ni—Rh does not exhibit any dramatic behavior and is in the main quite well-behaved. Further, one should note that the thermoelectric power is negative for Ni—Cu and positive for Ni—Rh alloys. The usual explanation for this in terms of a rigid band model is that for transition metals the s—d interband scattering term in the thermoelectric power can dominate, and this term gives a positive or negative contribution depending on whether the d-band density of states near the Fermi energy is increasing or decreasing with energy. As discussed further below, however, it is very unlikely that a band model is even approximately relevant for these alloys. A small anomaly in the thermoelectric power of Ni—Cu occurs at about 50°K, which is the temperature range in which there is a low temperature minimum in 8’9 that the effects minimum the resistivity. This suggests that the two are in related. It has at been the resistivity lowsuggested temperatures arises from spin—ifip scattering of conduction electrons from rigid spin clusters, analogous to Kondo scattering in alloys contaming dilute concentrations of impurity atoms which have a localized moment. One might then expect a contribution to the thermoelectric power which also arises from spin—flip scattering of electrons. This process gives rise in very dilute Kondo alloys to a peak in the thermoelectric power at a temperature which independent of magnetic impurity concentration.24 Susceptibility experiments2 indicate that the concentration of clusters in Ni—Cu is in fact quite low and increases gradually as one approaches the critical composition. In the present experiment we observe an anomaly in the thermoelectric
3
power at about 50°K independent of alloy composition. The fact that the temperature at which the effect occurs stays roughly the same as the cluster concentration varies is thus consistent with the above suggestion. On the other hand, it is intriguing to note that Taylor and Coles25 observed an anomalous temperature dependence for the thermoelectric power of Pd.,~Ag~ similar to what we have found for Ni—Cu. This anomaly was observed in the vicinity of 120°K, and was not in evidence in Pd 44 Ag54 or Pd~Ag.~, the nearest compositions measured. Thus, both the resistivity and the thermoelectric power of the two isoelectronic systems Pd—Ag and Ni—Cu are quite similar, suggesting that they may in fact derive from the same or related causes. Since Pd—Ag does not have spin clusters, the behavior of this system cannot be magnetic in origin. Ahmed and Greig’° propose an explanation for the resistivity based on a band model description, where the two minima arise from temperature dependent s—d interband scattering; they also suggest that the same mechanism may play a 26 however, indicate role in Ni—Cu. Various experiments, that local phenomena predominate in both alloy systems, and that the alloys are essentially described by a superposition of bands appropriate to the two separate constituent metals. Further, a rigid band description of the type proposed by Ahmad and Greig,’°even when modified as they suggest by variations on a local scale, would lead to temperature (i.e. energy) dependences which vary considerably with composition, particularly in light of the presence of an almost filled d-band. Instead, the thermoelectric power exhibits a change in slope at approximately the same temperature of 50°K for a fairly wide range of Ni—Cu compositions. This strongly suggests that the relevant process is local, and not consistent with a band description. In this connection, it would be interesting to obtain measurements for Pd—Ag alloys with compositions close to Pd 60Ag.~. In closing, one should note that the resistivity anomalies in Ni—Cu are an order of magnitude larger than in Pd—Ag, and the anomalies in both the resistivity and thermoelectric power persist over a wide range of Ni—Cu compositions. One should not overlook the possibility that more than one mechanism plays a role in Ni—Cu. Thus, the behavior of Ni—Cu may be determined both by effects due to spin clusters and by a mechanism which is common to Ni—Cu and Pd—Ag.
Acknowledgements The authors are indebted to the referee for his valuable and constructive comments, and for pointing out an erroneous assumption in an earlier version of this article. We also thank Professors Frederick W. Smith and James S. Kouvel for many helpful discussions. —
4
THERMOELECTRIC POWER OF NiCu AND NiRh ALLOYS
vol. 20, No. 1
REFERENCES 1.
HICKS T.J., RAINFORD B., KOUVEL J.S., LOW G.G. & COMLY i.E.,Phys. Rev. Letr. 22,531(1969).
2. 3.
4.
KOUVEL J.S. & COMLY J.B., Phys. Rev. Lett. 24, 598 (1970). MUELLNER W.C. & KOUVEL J.S.,Magnetism and Magnetic Materials 1971 (Edited by GRAHAM C.D. Jr. & RHYNE J.J.) p. 487. AlP Conf. Proc., New York, (1972); MUELLNER W.C. & KOUVEL J.S., Phys. Rev. B! 1, 4552 (1975). HOUGHTON R.W., SARACHIK M,P. & KOUVEL J.S., Solid State Commun. 8,943(1970).
5. 6.
SKOSKIEWICZ T. & BARANOWSKI B., Solid State Commun. 7,647(1969). CRANGLE J. & BUTCHER P.J.L.,Phys. Lett. A32, 80(1970).
7.
HOUGHTON R.W., SARACHIK M.P. & KOUVEL J.S., Phys. Rev. Lett. 25, 238 (1970).
8.
LEVIN K. & MILLS D.L.,Phys. Rev. 89,2354(1974).
—
9. 10.
FIBICH M. & RON A., J. Phys. 32, C1-748 (1971). MIMAD H.M. & GREIG D.,Phys. Rev. Lett. 32,833(1974).
11.
HOUGHTON R.W., SARACHIK M.P. & KOUVEL J.S., Solid State Commun. 10,369(1972).
12. 13.
AMAJ1OU A., GAUTIER F. & LOEGEL B.,J. Phys. 35, C4-217 (1974). COLES B.R.,Phys. Lett. 8,243 (1964).
14.
SARACHIK M.P., Phys. Rev. 170, 679 (1968).
15. 16.
SCHINDLER A.I. & RICE M.J.,Phys. Rev. 164,759(1967). LEDERER P. & MILLS D.L.,Phys. Rev. 165,837 (1968).
17. 18.
KAISER A.B. & DONIACH S.,Int. J. Magn. 1, 11(1970). ZRUDSKY D.R. & SHOWALTER A.B.,Phys. Lett. 45A, 105 (1973).
19. 20.
LEGVOLD S., PETERSON D.T., BURGARDT P., HOFER R.J., LUNDELL B. & VYROSTEK T.A., Phys. Rev. B9, 2386 (1974). SCHROEDER P.A., WOLF R. & WOOLLAM J.A.,Phys. Rev. 138, A105 (1965).
21.
AHMAD H.M. & GREIG D.,J. Phys. 35, C4-223 (1974).
22. 23.
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